Solve sqrt{8}+sqrt{12}+sqrt{18}

$$\sqrt{ 8 } + \sqrt{ 12 } + \sqrt{ 18 }$$

Evaluate

$$\sqrt{2}\left(\sqrt{6}+5\right)\approx 10.535169427$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{12}+\sqrt{18}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{2}+2\sqrt{3}+\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{2}+2\sqrt{3}+3\sqrt{2}$$

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+2\sqrt{3}$$